# The method of determining the position of the coordinate axes of the inertial navigation system of the object relative to the base coordinate system (and its variants)

(57) Abstract:

The invention relates to the field of navigation of various objects having onboard inertial navigation system (aircraft, spacecraft, automobiles, ships). The proposed method includes the navigation measurement in the base and inertial coordinate systems of the object. As a basic choose the one that is used in global navigation system "GLONASS" and "Navstar". In different pairs of time points on a consistent and non-parallel portions of the trajectory measured coordinates and/or velocity vectors of the object in both coordinate systems. While these motion parameters determined by measuring the acceleration vector in these areas. The coordinates and/or velocities in areas determine the trajectory of the moving object and/or increment its speed. Them build the transition matrix between the base and inertial coordinate systems. Components of a matrix find the relative position of the coordinate axes of both systems. Non-parallel parts of the trajectory can be obtained by a special maneuver of the object. The invention improves accuracy and provides all-weather its implementation. 3 S. and 1 C.p. f-crystals, 1 Il. Such objects may include terrestrial and marine vehicles (cars, ships), as well as air and space vehicles (aircraft, missiles, space vehicles).There is a method of determining the position of the triaxial navigation system for the simultaneous measurement of the gravitational acceleration and the angular velocity of rotation of the Earth [1].The method is used primarily for initial exhibition inertial stationary relative to the Earth objects, and the base will often accept a geographic coordinate system. The method cannot be applied to moving objects, experiencing acceleration and angular velocity.There is a method of determining the position of the triaxial navigation system relative to the base coordinate system is known optical directions [2].The method is used as for the initial exhibition of the axes of the navigation system stationary objects by well-known destinations, such as the selected stars, and in the process of movement of the object.There is also known a method astronavigation in patent N 2033949 RF (MKI^{6}B 64 G, 1/24) comprising the combination of a common plane chustvitelnos the if-device-polar star" (based on the measured angular misalignments along the channels of the pitch, yaw and roll) to determine an inertial longitude of the location apparatus according to the azimuth angle in the field of view of the star sensor is selected stars around the device-polar star" in relation to the base frame, and taking into account inertial longitude of the base, the parameters of which are remembered. When this base reference plane containing the device-polar star" and "the device is a navigation star", is characterized by inertial longitude equal to the right ascension of the pole star, and deployed relative to the General plane of the sensitivity of the sensors of the Earth and the Polar star by an angle equal to the angle between the plane containing the direction of the center of the Earth-the North star" and "the center of the Earth pole of the World" and the plane containing the direction of the center of the Earth-the North star" and "the center of the Earth-navigation star.However, these methods require the presence on Board of an object optical means, for example, astrovision, and compliance with the terms of the visibility of optical landmarks. For ground targets and aircraft in the atmosphere is affected by weather conditions, the use of optical means restricts the use of the method.The closest analogue printline base coordinate system is the way based on the simultaneous measurement of the acceleration vector in the base and defined systems [3]. Moreover, the vector acceleration is measured at least at two points of the trajectory, where the measured acceleration vector are not parallel.The method can be used only in those cases where the base coordinate system and the coordinate system of the object experiencing the same acceleration, i.e. the carrier base system and the object are connected mechanically and moving along a single trajectory. For example, the plane (the object) on the deck of an aircraft carrier (the carrier of the base system), rocket (object) aboard the aircraft carrier (the carrier of the base system).The method has practical implications in cases when the underlying coordinate system is known with better accuracy than the coordinate system of the object, and when the accuracy of the underlying coordinate system sufficient to perform the navigation task object.In practice, these conditions are not met and the method cannot be applied, for example, the booster should have a precision alignment of the inertial system is not worse than the units of arc minutes, while the aircraft carrier to launch the rocket may be the orientation of the axes of the base system POS is E. the accuracy and reliability of positioning the coordinate axes of the inertial navigation system of a moving object, providing all-weather this definition.This task is achieved in that in the method according to option 1 determine the position of the coordinate axes of the inertial navigation system of the object relative to the base coordinate system, including navigation measurement object moving in inertial space, in the base coordinate system and the inertial coordinate system of the object

- at time t

_{i}and t

_{i+1}measure the coordinates of a moving object in the coordinate system Global navigation system "GLONASS" or/and "Navstar", is selected as the base coordinate system;

- on the trajectory of the object t

_{i}- t

_{i+1}measure the acceleration vector in the inertial coordinate system of the object, which determines the coordinates of the object in the same moments of time t

_{i}and t

_{i+1};

- at time t

_{j}and t

_{j+1}on the trajectory of the object is not parallel to the plot of the previous navigation measurements, carried out similar measurements of the coordinates of the object in the base coordinate system and the inertial coordinate system of the object;

- then according to the received coordinates for each trajectory t

_{i}- t

_{i+1}and t

_{j}- t

_{j+1}, Etime coordinates L

_{i}

^{B}, L

_{j}

^{B}and in the inertial coordinate system of the object, L

_{i}

^{U}, L

_{j}

^{U};

then determine the transition matrix between the base coordinate system and the inertial coordinate system of the object from the system of equations

L

_{i}

^{B}=AL

_{i}

^{U},

L

_{j}

^{B}=AL

_{j}

^{U},

i,j = 1...n, i j,

where A is the transition matrix from the base coordinate system to the inertial coordinate system of the object,

n - number of lots trajectory;

- components of the matrix A determine the position of the coordinate axes of the inertial navigation system of the object relative to the base.In the proposed method according to option 2 determine the position of the coordinate axes of the inertial navigation system of the object relative to the base coordinate system, including navigation measurement object moving in inertial space, in the base coordinate system and the inertial coordinate system of the object

in moments temporizing t

_{i}and t

_{i+1}measure the velocity vector of a moving object in the coordinate system Global navigation system "GLONASS" or/and "Navstar", is selected as the base coordinate system;

on ucast, which determine the velocity vector of the object in the same moments of time t

_{i}and t

_{j+1};

- at time t

_{j}and t

_{j+1}on the trajectory of the object is not parallel to the plot of the previous navigation measurements, carried out similar measurements of the velocity vector of the object in the base coordinate system and the inertial coordinate system of the object;

- then on the obtained velocity vectors at each trajectory t

_{i}-t

_{i+1}and t

_{j}-t

_{j+1}preferred, at least two, determine the increment of the velocity vector object V

_{i}V

_{j}in the base coordinate system V

_{i}

^{B},

V

_{j}

^{B}and in the inertial coordinate system of the object V

_{i}

^{U}V

_{j}

^{U};

- then determine the transition matrix between the base coordinate system and the inertial coordinate system of the object from the system of equations

V

_{i}

^{B}= AV

_{i}

^{U},

V

_{j}

^{B}= AV

_{j}

^{U},

i, j = 1...n, i j,

where A is the transition matrix from the base coordinate system to the inertial coordinate system of the object,

n - number of lots trajectory;

- components of the matrix A determine the position of the axes of coordinates initializemenu position coordinate axes of the inertial navigation system of the object relative to the base coordinate system, including navigation measurement object moving in inertial space, in the base coordinate system and the inertial coordinate system of the object

- at time t

_{i}and t

_{i+1}measure the position and velocity vector of a moving object in the coordinate system Global navigation system "GLONASS" or/and "Navstar", is selected as the base coordinate system;

- on the trajectory of the object t

_{i}-t

_{i+1}measure the acceleration vector in the inertial system of coordinates, which define the coordinates and the velocity vector of the object in the same moments of time t

_{i}and t

_{i+1};

- at time t

_{j}and t

_{j+1}on the trajectory of the object is not parallel to the plot of the previous navigation measurements, carried out similar measurements of coordinates and velocity vector of the object in the base coordinate system and the inertial coordinate system of the object;

- then on the obtained coordinates and velocity vectors at each trajectory t

_{i}-t

_{i+1}and t

_{j}-t

_{j+1}preferred, at least two, determine the displacement vector of the object L

_{i}, L

_{j}and the increment of the vector of its velocity V

_{i}V

_{j}in the base system NAT object L

_{i}

^{U}, L

_{j}

^{U}V

_{i}

^{U}V

_{j}

^{U};

- then determine the transition matrix between the base coordinate system and the inertial coordinate system of the object from the system of equations

L

_{i}

^{B}= AL

_{i}

^{B}V

_{i}

^{B}= AV

_{i}

^{U},

L

_{j}

^{B}= AL

_{j}

^{U}V

_{j}

^{B}= AV

_{j}

^{U},

i, j = 1...n, i j,

where A is the transition matrix from the base coordinate system to the inertial coordinate system of the object,

n - number of lots trajectory;

- components of the matrix A determine the position of the coordinate axes of the inertial navigation system of the object relative to the base.In the proposed method when the object is moving in inertial space on a straight-line trajectory carry out his maneuver that implements at least two non-parallel portion of the trajectory on which the conduct mentioned navigation measurements.The essence of the proposed method is illustrated on the drawings, where:

1 - object;

2 - axis inertial navigation system object X

^{U}, Y

^{U}, Z

^{U};

3 - axis coordinate of the base system, X

^{B}, Y

^{B}, Z

^{B};

4 - global which define the coordinates of a moving object in the base coordinate system type "GLONAS" or/and "Navstar" and in the inertial coordinate system of the object;

L

_{1}, L

_{j}the displacement vector of the object respectively on the trajectory t

_{i}- t

_{i+1}and t

_{j}-t

_{j+1},

V

_{i}V

_{j}- the increment of the velocity vector of the object respectively on the trajectory t

_{i}-t

_{i+1}and t

_{j}-t

_{j+1};

that is, the angles that define the position of the axes of coordinates of the inertial navigation system of the object and X

^{U}, Y

^{U}, Z

^{U}with respect to the axes of coordinates of the underlying system X

^{B}, Y

^{B}, Z

^{B}(the Euler angles).The method differs from the known analogues that in option 1

- at time t

_{1}and t

_{i+1}measure the coordinates of a moving object 1 in the coordinate system of the 3 Global navigation system 4, is selected as the basic coordinate system [4];

in the same moments of time t

_{i}and t

_{i+1}define the same coordinates of the object 1 in the inertial navigation system of coordinates of the object 2 according to the measurements of the acceleration vector on the trajectory t

_{i}-t

_{i+1};

- at time t

_{j}and t

_{j+1}on the trajectory of the object 1 that is not parallel to the plot of the previous navigation measurements produce similar measurements of the coordinates of the object in the base coordinate system 3 and inective t

_{i}-t

_{i+1}and t

_{j}-t

_{j+1}preferred, at least two, determine the displacement vector L

_{i}, L

_{j}in the base coordinate system 3 L

_{i}

^{B}, L

_{j}

^{B}and in the inertial coordinate system of the object 2L

_{i}

^{U}, L

_{j}

^{U}.then determine the angles of misalignment between the base coordinate system 3 and the inertial coordinate system of the object 2 from the system of equations

L

_{i}

^{B}=AL

_{i}

^{U},

L

_{j}

^{B}=AL

_{j}

^{U},

i,j=1...n, i,j j

where A is the transition matrix from the base coordinate system 3 in the inertial coordinate system of the object 2,

n is the number of plots trajectories;

- received components of the transition matrix And determine the position of the coordinate axes of the inertial navigation system of the object 2 relative to the base 3; that is, determine the angles of misalignment between them, (the Euler angles).The method is also distinguished by the fact that in option 2

- at time t

_{i}and t

_{i+1}measure the velocity vector of the moving object 1 in the coordinate system of the 3 Global navigation system 4 type "GLONAS" or/and "Navstar") selected as the base coordinate system;

- on the trajectory opredelyaut the velocity vector of the object in the same moments of time t

_{i}and t

_{i+1};

- at time t

_{j}and t

_{j+1}on the trajectory of the object is not parallel to the plot of the previous navigation measurements, carried out similar measurements of the velocity vector of the object in the base coordinate system 3 and in the inertial coordinate system of the object 2;

- then on the obtained velocity vectors at each trajectory t

_{i}-t

_{i+1}and t

_{j}-t

_{j+1}preferred, at least two, determine the increment of the velocity vector object V

_{i}V

_{j}in the base coordinate system 3 V

_{i}

^{B}V

_{j}

^{B}and in the inertial system of coordinates 2 object V

_{i}

^{U}V

_{j}

^{U}; - and then determine the transition matrix between the base coordinate system 3 and the inertial coordinate system 2 object from the system of equations:

V

_{i}

^{B}= AV

_{i}

^{U},

V

_{j}

^{B}= AV

_{j}

^{U},

i,j=1...n, i j,

where A is the transition matrix from the base coordinate system to the inertial coordinate system of the object,

n - number of lots trajectory;

- components of the matrix A determine the position of the coordinate axes of the inertial navigation system 2 of the object relative to the base 3.Offe the velocity vector of the moving object 1 in the coordinate system of the Global positioning system, 4 "GLONAS" or/and "Navstar", selected as the base coordinate system;

- on the trajectory of the object t

_{i}-t

_{i+1}measure the acceleration vector in the inertial coordinate system 2 objects, which define the coordinates and the velocity vector of the object 1 in the same moments of time t

_{i}and t

_{i+1};

- at time t

_{j}and t

_{j+1}on the trajectory of the object 1 that is not parallel to the plot of the previous navigation measurements, have the same coordinates and velocity vector of the object in the base coordinate system 3 and in the inertial coordinate system of the object 2;

- then on the obtained coordinates and velocity vectors at each trajectory t

_{i}-t

_{i+1}and t

_{j}+t

_{j+1}preferred, at least two, determine the displacement vector of the object L

_{i}, L

_{j}and the increment of the vector of its velocity V

_{i}V

_{j}in the base coordinate system 3 L

_{i}

^{B}, L

_{j}

^{B}V

_{i}

^{B}V

_{j}

^{B}and in the inertial coordinate system 2 object 1 L

_{i}

^{U}, L

_{j}

^{U}V

_{i}

^{U}V

_{j}

^{U};

- then determine the transition matrix between the base coordinate system 3 and the inertial coordinate system 2 of the object 1 from the system EQ

^{U}V

_{j}

^{B}= AV

_{j}

^{U}< / BR>

i,j = 1...n, ij,

where A is the transition matrix from the base coordinate system to the inertial coordinate system of the object,

n - number of lots trajectory;

- components of the matrix A determine the position of the coordinate axes of the inertial navigation system 2 of the object relative to the base 3.The method is also characterized in that the motion of the object 1 in inertial space on a straight-line trajectory, carry out his maneuver that implements at least two non-parallel portion of the trajectory on which the conduct of the navigation measurement.The proposed method of determining the position of the coordinate axes of the navigation system of a moving object allows you to determine with high accuracy (a few meters) large moving objects (thousands of kilometers) in all weather conditions with the help of Global positioning systems "GLONAS" or/and "Navstar", working in the radio.For example, for such moving objects such as aircraft, missiles, space vehicles whose movements are significant, the accuracy of determining the position of the coordinate axes of their navigation systems may be units of angular avstar", unlike astronavigation systems, provides a method of high reliability and all-weather. An example implementation of the proposed method of determining the position of the coordinate axes of the inertial navigation system of the object can serve as aerospace system that uses the serial aircraft carrier and run with their side boosters. The aircraft carrier, as a rule, have the navigation system with the accuracy of the orientation axes, reaching tens of arc minutes, which is insufficient for starting with his side of the booster, the accuracy of the orientation axes of the navigation system which should not be lower units of arc minutes, which is achieved by the proposed method.Literature

1. G. A. Khlebnikov "Initial exhibition inertial navigation systems", Military Academy of the name of F. E. Dzerzhinsky, M., 1994, pp. 225-228.2. Same, pages 230-231.3. The same, page 237.4. "Radio systems" Ed. by Y. M. Kazarinov, M.: Vysshaya SHKOLA, 1990, pp. 304-306. 1. The method of determining the position of the coordinate axes of the inertial navigation system of the object relative to the base coordinate system, including navigation measurement object, dvizhushchimisya fact, that at time t

_{i}and t

_{i+1}measure the coordinates of a moving object in the coordinate system global navigation system "GLONASS" or/and "Navstar", is selected as the base coordinate system; on the trajectory of the object in time t

_{i}- t

_{i+1}measure the acceleration vector in the inertial coordinate system of the object, which determines the coordinates of the object in the same moments of time t

_{i}and t

_{i+1}; at time t

_{j}and t

_{j+1}on the trajectory of the object is not parallel to the plot of the previous navigation measurements, carried out a similar definition of the object coordinates in the base coordinate system and the inertial coordinate system of the object; then according to the received coordinates for each of the at least two sections of the trajectory in the time periods t

_{i}- t

_{i+1}and t

_{j}- t

_{j+1}define the vectors of the moving object in the base (L

_{i}

^{B}, L

_{j}

^{B}) and inertial (L

_{i}

^{U}, L

_{j}

^{U}) coordinate systems of the object, and then determine the matrix (A) transition between the base coordinate system and the inertial coordinate system of the object from the system of equations

L

_{i}

^{B}= AL

_{i}

^{U},

L

_{j}

^{ the matrix A determine the position of the coordinate axes of the inertial navigation system of the object relative to the base.2. The method of determining the position of the coordinate axes of the inertial navigation system of the object relative to the base coordinate system, including navigation measurement object moving in inertial space, in the base coordinate system and the inertial coordinate system of the object, characterized in that at time tiand ti+1measure the velocity vector of a moving object in the coordinate system global navigation system "GLONASS" or/and "Navstar", is selected as the base coordinate system; on the trajectory of the object in time ti- ti+1measure the acceleration vector in the inertial coordinate system of the object, which determine the velocity vector of the object in the same moments of time tiand ti+1; at time tjand tj+1on the trajectory of the object is not parallel to the plot of the previous navigation measurements, carried out a similar definition of the velocity vector of the object in the base coordinate system and the inertial coordinate system of the object; then the resulting velocity vectors at each of the at least two sections of the trajectory in the time periods ti- ti+1and tj- tj+1define increment the SUB>U) coordinate systems of the object, and then determine the transition matrix (A) between the base coordinate system and the inertial coordinate system of the object from the system of equationsViB= AViU,VjB= AVjU,i, j = 1 ... n, i j,where n is the number of sections of the path,thus the components of the matrix A determine the position of the coordinate axes of the inertial navigation system of the object relative to the base.3. The method of determining the position of the coordinate axes of the inertial navigation system of the object relative to the base coordinate system, including navigation measurement object moving in inertial space, in the base coordinate system and the inertial coordinate system of the object, characterized in that at time tiand ti+1measure the position and velocity vector of a moving object in the coordinate system global navigation system "GLONASS" or/and "Navstar", is selected as the base coordinate system; on the trajectory of the object in time ti- ti+1measure the acceleration vector in the inertial system of coordinates, which define the coordinates and vector RMSE is actorii object, not parallel to the plot of the previous navigation measurements, have the same coordinates and velocity vector of the object in the base coordinate system and the inertial coordinate system of the object; then the obtained coordinates and velocity vectors at each of the at least two sections of the trajectory in the time periods ti- ti+1and tj- tj+1define the vectors of displacement and velocity increment object in basic (respectively, LiB, LjBand ViBVjB) and inertial (respectively, LiU, LjUand ViUVjU) coordinate systems of the object, and then determine the transition matrix (A) between the base coordinate system and the inertial coordinate system of the object from the system of equationsLiB= ALiUViB= AViU,LjB= ALjUVjB= AVjU,i, j = 1 ... n, i j,where n is the number of sections of the path,thus the components of the matrix A determine the position of the coordinate axes of the inertial navigation system of the object relative to the base.4. The method according to any of paragraphs.1 to 3, the keys of his maneuver, implements at least two non-parallel portion of the trajectory on which the conduct of the navigation measurement. }

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